A view of canonical extension

This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties are given. In particular, they are doubly algebraic lattices and their interval topologies agree with their double Scott topologies and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi Symposium on Language, Logic and Computation Bakuriani, Georgia, September 21-25 200

Uniform interpolation and coherence

A variety V is said to be coherent if any finitely generated subalgebra of a finitely presented member of V is finitely presented. It is shown here that V is coherent if and only if it satisfies a restricted form of uniform deductive interpolation: that is, any compact congruence on a finitely generated free algebra of V restricted to a free algebra over a subset of the generators is again compact. A general criterion is obtained for establishing failures of coherence, and hence also of uniform deductive interpolation. This criterion is then used in conjunction with properties of canonical extensions to prove that coherence and uniform deductive interpolation fail for certain varieties of Boolean algebras with operators (in particular, algebras of modal logic K and its standard non-transitive extensions), double-Heyting algebras, residuated lattices, and lattices

Modular Construction of Complete Coalgebraic Logics

We present a modular approach to defining logics for a wide variety of state-based systems. The systems are modelled by coalgebras, and we use modal logics to specify their observable properties. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular fashion. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems, for which no complete axiomatisation has been obtained so far

Wireless and Physical Security via Embedded Sensor Networks

Wireless Intrusion Detection Systems (WIDS) monitor 802.11 wireless frames (Layer-2) in an attempt to detect misuse. What distinguishes a WIDS from a traditional Network IDS is the ability to utilize the broadcast nature of the medium to reconstruct the physical location of the offending party, as opposed to its possibly spoofed (MAC addresses) identity in cyber space. Traditional Wireless Network Security Systems are still heavily anchored in the digital plane of "cyber space" and hence cannot be used reliably or effectively to derive the physical identity of an intruder in order to prevent further malicious wireless broadcasts, for example by escorting an intruder off the premises based on physical evidence. In this paper, we argue that Embedded Sensor Networks could be used effectively to bridge the gap between digital and physical security planes, and thus could be leveraged to provide reciprocal benefit to surveillance and security tasks on both planes. Toward that end, we present our recent experience integrating wireless networking security services into the SNBENCH (Sensor Network workBench). The SNBENCH provides an extensible framework that enables the rapid development and automated deployment of Sensor Network applications on a shared, embedded sensing and actuation infrastructure. The SNBENCH's extensible architecture allows an engineer to quickly integrate new sensing and response capabilities into the SNBENCH framework, while high-level languages and compilers allow novice SN programmers to compose SN service logic, unaware of the lower-level implementation details of tools on which their services rely. In this paper we convey the simplicity of the service composition through concrete examples that illustrate the power and potential of Wireless Security Services that span both the physical and digital plane.National Science Foundation (CISE/CSR 0720604, ENG/EFRI 0735974, CIES/CNS 0520166, CNS/ITR 0205294, CISE/ERA RI 0202067